How do I find the reference angle in radicals given the value of cosecant 5 pi/6?

Answer 1

If the given angle is θ, and the reference angle is Ø, then Ø is always in QI.

If θ is in Q1, Ø = θ
in QII, Ø = π-θ
in QIII, Ø = θ-π
in QIV, Ø = 2π-θ

so, in this case, your reference angle is pi - 5pi/6 = pi/6